Arrow-Debreu

Summary

AS=AD for every commodity in the economy.......................

Assumptions

  • Part of the Walrasian heritage. 
  • Two basic principles
    1. Optimizing behaviour on the part of individual entities in the presence of prices taken as given.
    2. Setting of prices so that, given this individual behaviour, S=D in each market.
  • Three ways to include money:
    1. Overlapping generations - money is a device for accomplishing inter temporal reallocation of consumption - young people save, old people spend.
    2. Money in the utility function - lowest liquidity costs - particularly the question of whether money yields utility directly or indirectly through lower transaction costs.
    3. Cash-in-advance models - where cash is required to undertake transactions and this is a constraint rather than in the utility function.

Model/Theory

  • Firms maximise profits by choosing inputs and outputs subject to prices
  • Consumers maximise utility from consumption subject to a budget constraint which is consumption = endowment + profits
  • Equilibrium properties:
    1. Not unique as equations are homogenous (therefore can have multiples of the price level)
    2. Walras' Law defines the linear dependence among the n equations.
    3. Difference between temporary and full (Arrow-Debreu) equilibrium where all goods can be exchanged now via a set of futures markets and the implied future savings/investment decisions.

Predictions

Evidence

Evaluation

  • As Keynes said saving although the abstinence from current consumption offers no signals for future consumption and thus has a depressing effect on employment.
  • Problem with Arrow-Debreu system is there is no role for money. 
  • However, as a method for intertemporal transfers return-bearing assets are superior to money and argubably if an economy is of a finite duration then money will lose its ability to hold value. 
  • One problem with cash in advance is that it requires two constraints making it not obviously superior to a barter world (Clower dilemma). Though this is usually dealt with by 1. transaction costs & imperfect info 2. legal restrictions or social/institutional arrangements.